∵∶∶ a =2 2∶∶∶ b =3 ∴a? B/ 冘冘冘冘 (A and B are vectors) = COS60.

∴ab=3

∴乸Ma+Nb 乸 =m? Answer? +n？ b？ +2mnab a？ = 丨 a 丨? =4 b？ =?·?？ =9 ab=3

=4m？ +9n？ +6mn

Because 1≤m≤2 and 0≤n≤2, when m=2 and n=2, what about ma+nb? There is a maximum value.

Maximum value =4×4+4×9+6×2×2=76.

So the maximum value of ma+nb is √76=2√ 19.

I'm happy to answer your question. I wish you progress in your study! You can ask questions if you don't understand! If you agree with my answer. Please click the "Select Satisfied Answer" button below. If you have any other questions, please send them separately or click to ask me for help. Not easy to answer, please understand, thank you!